Packing 4-Partite Tree into Complete 4-Partite Graph

Abstract

For graphs G and H, an embedding of G into H is an injection [see formula in PDF] such that [see formula in PDF] whenever [see formula in PDF]. A packing of p graphs [see formula in PDF] into [see formula in PDF]is a p-tuple [see formula in PDF] such that, for [see formula in PDF], [see formula in PDF] is an embedding of [see formula in PDF] into H and the p sets [see formula in PDF] are mutually disjoint. Motivated by the "Tree Packing Conjecture" made by Gy[see formula in PDF]rf[see formula in PDF]s and Lehel, Wang Hong conjectured that for each k-partite tree, there is a packing of two copies of [see formula in PDF] into a complete k-partite graph [see formula in PDF], where [see formula in PDF]. In this paper, we confirm this conjecture for [see formula in PDF].